Transformation Groups and Representation Theory
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766 Tammo tom Dieck
Transformation Groups and Representation Theory
Springer-Verlag Berlin Heidelberg New York 1979
Author T. tom Dieck Mathematisches Institut Bunsenstra6e 3 - 5 D-3400 G6ttingen
AMS Subject Classifications (1970): 20C10, 20 C15, 20 D15, 55-02, 55 B25, 5 5 E 5 0 , 57-02, 57 D85, 57 E15, 5 7 E 2 5
ISBN 3-540-09720-1 Springer-Verlag Berlin Heidelberg NewYork ISBN 0-387-09720-1 Springer-Verlag NewYork Heidelberg Berlin Library of Congress Cataloging in PublicationData Dieck, Tammotom. Transformationgroups and representationtheory. (Lecture notes in mathematics;766) Bibliography: p. Includes index. 1. Topological transformationgroups. 2.'Representationsof groups. I. Title. IL Series: Lecture notes in mathematics(Berlin); 766. QA3.L28 no. 766 [QA613.7] 510'.8s [514'.223] ?9-24606 ISBN 0-387-09720-1 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin Heidelberg 1979 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210
Preface These
are
which
I gave
summer
extended
term
ring and reader
at t h e M a t h e m a t i c a l
of t h e s e
of t r a n s f o r m a t i o n
is a c q u a i n t e d
presentation
Section
and m a d e
for a c o u r s e Institute
on transformation
at G ~ t t i n g e n
are many
and
elementary
II c o n t a i n s
due
is to g i v e
an i n t r o d u c t i o n
groups
centers
of group with
theory,
some
My thanks
typed
notes
the topology
presented
notes
during
groups the
1978.
The purpose the t h e o r y
lecture
material
transformation topics
to C h r i s t i a n
the m a n u s c r i p t .
representations.
the b a s i c
joint work
valuable
which
to t h a t p a r t
around
It is a s s u m e d
in a l g e b r a i c
groups.
the
of
Burnside that
the
topology,
Nevertheless
re-
we have
in d e t a i l .
with
Henning
Okonek
suggestions
and
who
Hauschild.
read
part
to M a r g r e t
of the m a n u s c r i p t
Rose
Schneider
who
Contents
The B u r n s i d e
i.I
Finite
1.2
The B u r n s i d e
1.3
Congruences
1.4
Idempotent
1.5
Units
1.6
Prime
1.7.
An example:
1.8.
Comments
Ii
1.9.
Exercises
12
2.
The J - h o m o m o r p h i s m
2.1.
The J - h o m o m o r p h i s m
2.2.
Quadratic
2.3.
The q u a d r a t i c
2.4.
Comments
25
2.5.
Exercises
25
-rings
27
3.
ring of finite
1
io
G-sets
1
G-sets
1
ring A(G) between
fixed p o i n t
4
numbers
7
elements
8 9
ideals The a l t e r n a t i n g
forms
iO
group A 5
and q u a d r a t i c
14
forms
14
on t o r s i o n
groups.
Gau~
sums
15 22
J-h
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